<p>Cross-collection topic models (ccTMs) aim to learn both shared and collection-specific topics across multiple document collections. Many ccTMs are built on cross-collection Latent Dirichlet Allocation and use Dirichlet priors, which impose a restrictive covariance structure on topic proportions and topic-word distributions. In addition, several ccTMs rely on exact topic-index alignment across collections, which can be too rigid when collections differ in theme coverage. We propose GD-BL ccTM, a cross-collection topic model that uses a Generalized Dirichlet (GD) prior for document-topic proportions and a Beta-Liouville (BL) prior for topic-word distributions. These priors allow a less restrictive covariance structure, improving modeling of topic co-occurrence and word dependencies. GD-BL ccTM also relaxes strict alignment by separating shared global topics from collection-specific topics and using a token-level selector to route each word to the shared or collection-specific component. We evaluate GD–BL ccTM on real-world datasets for comparative text mining and cross-domain classification. Results show consistent improvements over competitive baselines in perplexity, topic coherence, and classification accuracy, supporting the benefits of flexible priors and relaxed alignment in cross-collection settings.</p>